How can I get vertex painted .obj files to import into Blender?
june 2015:

Vertex Colors are not part of the .obj file type specification - see section on Geometric Vertex.

However some programs use an unofficial extended format for inter-change and add r,g,b information on the same line as the vertex coordinates.

# standard format (v: x y z)
v 1.0 1.2 0.3 

# extended format (v: x y z r g b)
v 1.0 1.2 0.3 0.5 0.2 0.2


Blender's .obj importer ignores everything after the x y z, therefore at this moment vertex colors are not parsed in any form.



If there was a color map (vertex colours) associated with the mesh, you'd  see it listed in 


menu: Properties -> tab: Data -> subheading: Vertex Colors


If there's nothing there then there's nothing to show.